Outcome predicted by a fitted model on a specified scale for a given combination of values of the predictor variables, such as their observed values, their means, or factor levels (a.k.a. "reference grid").

`predictions()`

: unit-level (conditional) estimates.`avg_predictions()`

: average (marginal) estimates.

The `newdata`

argument and the `datagrid()`

function can be used to control where statistics are evaluated in the predictor space: "at observed values", "at the mean", "at representative values", etc.

See the predictions vignette and package website for worked examples and case studies:

## Usage

```
predictions(
model,
newdata = NULL,
variables = NULL,
vcov = TRUE,
conf_level = 0.95,
type = NULL,
by = FALSE,
byfun = NULL,
wts = NULL,
transform = NULL,
hypothesis = NULL,
equivalence = NULL,
p_adjust = NULL,
df = Inf,
...
)
avg_predictions(
model,
newdata = NULL,
variables = NULL,
vcov = TRUE,
conf_level = 0.95,
type = NULL,
by = TRUE,
byfun = NULL,
wts = NULL,
transform = NULL,
hypothesis = NULL,
equivalence = NULL,
p_adjust = NULL,
df = Inf,
...
)
```

## Arguments

- model
Model object

- newdata
Grid of predictor values at which we evaluate predictions.

`NULL`

(default): Predictions for each observed value in the original dataset. See`insight::get_data()`

data frame: Predictions for each row of the

`newdata`

data frame.string:

"mean": Predictions at the Mean. Predictions when each predictor is held at its mean or mode.

"median": Predictions at the Median. Predictions when each predictor is held at its median or mode.

"marginalmeans": Predictions at Marginal Means. See Details section below.

"tukey": Predictions at Tukey's 5 numbers.

"grid": Predictions on a grid of representative numbers (Tukey's 5 numbers and unique values of categorical predictors).

`datagrid()`

call to specify a custom grid of regressors. For example:`newdata = datagrid(cyl = c(4, 6))`

:`cyl`

variable equal to 4 and 6 and other regressors fixed at their means or modes.See the Examples section and the

`datagrid()`

documentation.

- variables
Counterfactual variables.

Output:

`predictions()`

: The entire dataset is replicated once for each unique combination of`variables`

, and predictions are made.`avg_predictions()`

: The entire dataset is replicated, predictions are made, and they are marginalized by`variables`

categories.Warning: This can be expensive in large datasets.

Warning: Users who need "conditional" predictions should use the

`newdata`

argument instead of`variables`

.

Input:

`NULL`

: computes one prediction per row of`newdata`

Character vector: the dataset is replicated once of every combination of unique values of the variables identified in

`variables`

.Named list: names identify the subset of variables of interest and their values. For numeric variables, the

`variables`

argument supports functions and string shortcuts:A function which returns a numeric value

Numeric vector: Contrast between the 2nd element and the 1st element of the

`x`

vector."iqr": Contrast across the interquartile range of the regressor.

"sd": Contrast across one standard deviation around the regressor mean.

"2sd": Contrast across two standard deviations around the regressor mean.

"minmax": Contrast between the maximum and the minimum values of the regressor.

"threenum": mean and 1 standard deviation on both sides

"fivenum": Tukey's five numbers

- vcov
Type of uncertainty estimates to report (e.g., for robust standard errors). Acceptable values:

FALSE: Do not compute standard errors. This can speed up computation considerably.

TRUE: Unit-level standard errors using the default

`vcov(model)`

variance-covariance matrix.String which indicates the kind of uncertainty estimates to return.

Heteroskedasticity-consistent:

`"HC"`

,`"HC0"`

,`"HC1"`

,`"HC2"`

,`"HC3"`

,`"HC4"`

,`"HC4m"`

,`"HC5"`

. See`?sandwich::vcovHC`

Heteroskedasticity and autocorrelation consistent:

`"HAC"`

Mixed-Models degrees of freedom: "satterthwaite", "kenward-roger"

Other:

`"NeweyWest"`

,`"KernHAC"`

,`"OPG"`

. See the`sandwich`

package documentation.

One-sided formula which indicates the name of cluster variables (e.g.,

`~unit_id`

). This formula is passed to the`cluster`

argument of the`sandwich::vcovCL`

function.Square covariance matrix

Function which returns a covariance matrix (e.g.,

`stats::vcov(model)`

)

- conf_level
numeric value between 0 and 1. Confidence level to use to build a confidence interval.

- type
string indicates the type (scale) of the predictions used to compute contrasts or slopes. This can differ based on the model type, but will typically be a string such as: "response", "link", "probs", or "zero". When an unsupported string is entered, the model-specific list of acceptable values is returned in an error message. When

`type`

is`NULL`

, the default value is used. This default is the first model-related row in the`marginaleffects:::type_dictionary`

dataframe. See the details section for a note on backtransformation.- by
Aggregate unit-level estimates (aka, marginalize, average over). Valid inputs:

`FALSE`

: return the original unit-level estimates.`TRUE`

: aggregate estimates for each term.Character vector of column names in

`newdata`

or in the data frame produced by calling the function without the`by`

argument.Data frame with a

`by`

column of group labels, and merging columns shared by`newdata`

or the data frame produced by calling the same function without the`by`

argument.See examples below.

- byfun
A function such as

`mean()`

or`sum()`

used to aggregate estimates within the subgroups defined by the`by`

argument.`NULL`

uses the`mean()`

function. Must accept a numeric vector and return a single numeric value. This is sometimes used to take the sum or mean of predicted probabilities across outcome or predictor levels. See examples section.- wts
string or numeric: weights to use when computing average contrasts or slopes. These weights only affect the averaging in

`avg_*()`

or with the`by`

argument, and not the unit-level estimates themselves.string: column name of the weights variable in

`newdata`

. When supplying a column name to`wts`

, it is recommended to supply the original data (including the weights variable) explicitly to`newdata`

.numeric: vector of length equal to the number of rows in the original data or in

`newdata`

(if supplied).

- transform
A function applied to unit-level adjusted predictions and confidence intervals just before the function returns results. For bayesian models, this function is applied to individual draws from the posterior distribution, before computing summaries.

- hypothesis
specify a hypothesis test or custom contrast using a numeric value, vector, or matrix, a string, or a string formula.

Numeric:

Single value: the null hypothesis used in the computation of Z and p (before applying

`transform`

).Vector: Weights to compute a linear combination of (custom contrast between) estimates. Length equal to the number of rows generated by the same function call, but without the

`hypothesis`

argument.Matrix: Each column is a vector of weights, as describe above, used to compute a distinct linear combination of (contrast between) estimates. The column names of the matrix are used as labels in the output.

String formula to specify linear or non-linear hypothesis tests. If the

`term`

column uniquely identifies rows, terms can be used in the formula. Otherwise, use`b1`

,`b2`

, etc. to identify the position of each parameter. Examples:`hp = drat`

`hp + drat = 12`

`b1 + b2 + b3 = 0`

String:

"pairwise": pairwise differences between estimates in each row.

"reference": differences between the estimates in each row and the estimate in the first row.

"sequential": difference between an estimate and the estimate in the next row.

"revpairwise", "revreference", "revsequential": inverse of the corresponding hypotheses, as described above.

See the Examples section below and the vignette: https://vincentarelbundock.github.io/marginaleffects/articles/hypothesis.html

- equivalence
Numeric vector of length 2: bounds used for the two-one-sided test (TOST) of equivalence, and for the non-inferiority and non-superiority tests. See Details section below.

- p_adjust
Adjust p-values for multiple comparisons: "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", or "fdr". See stats::p.adjust

- df
Degrees of freedom used to compute p values and confidence intervals. A single numeric value between 1 and

`Inf`

. When`df`

is`Inf`

, the normal distribution is used. When`df`

is finite, the`t`

distribution is used. See insight::get_df for a convenient function to extract degrees of freedom. Ex:`slopes(model, df = insight::get_df(model))`

- ...
Additional arguments are passed to the

`predict()`

method supplied by the modeling package.These arguments are particularly useful for mixed-effects or bayesian models (see the online vignettes on the`marginaleffects`

website). Available arguments can vary from model to model, depending on the range of supported arguments by each modeling package. See the "Model-Specific Arguments" section of the`?marginaleffects`

documentation for a non-exhaustive list of available arguments.

## Value

A `data.frame`

with one row per observation and several columns:

`rowid`

: row number of the`newdata`

data frame`type`

: prediction type, as defined by the`type`

argument`group`

: (optional) value of the grouped outcome (e.g., categorical outcome models)`estimate`

: predicted outcome`std.error`

: standard errors computed using the delta method.`conf.low`

: lower bound of the confidence interval (or equal-tailed interval for bayesian models)`conf.high`

: upper bound of the confidence interval (or equal-tailed interval for bayesian models)`p.value`

: p value associated to the`estimate`

column. The null is determined by the`hypothesis`

argument (0 by default), and p values are computed before applying the`transform`

argument. For models of class`feglm`

,`Gam`

,`glm`

and`negbin`

, p values are computed on the link scale by default unless the`type`

argument is specified explicitly.

See `?print.marginaleffects`

for printing options.

## Details

For `glm()`

, `MASS::glm.nb`

, `gam::gam()`

, and `feols::feglm`

models with `type`

, `transform`

and `hypothesis`

all equal to `NULL`

(the default), `predictions()`

first predicts on the link scale, and then backtransforms the estimates and confidence intervals. This implies that the `estimate`

produced by `avg_predictions()`

will not be exactly equal to the average of the `estimate`

column produced by `predictions()`

. Users can circumvent this behavior and average predictions directly on the response scale by setting `type="response"`

explicitly. With `type="response"`

, the intervals are symmetric and may have undesirable properties (e.g., stretching beyond the `[0,1]`

bounds for a binary outcome regression).

## Standard errors using the delta method

Standard errors for all quantities estimated by `marginaleffects`

can be obtained via the delta method. This requires differentiating a function with respect to the coefficients in the model using a finite difference approach. In some models, the delta method standard errors can be sensitive to various aspects of the numeric differentiation strategy, including the step size. By default, the step size is set to `1e-8`

, or to `1e-4`

times the smallest absolute model coefficient, whichever is largest.

`marginaleffects`

can delegate numeric differentiation to the `numDeriv`

package, which allows more flexibility. To do this, users can pass arguments to the `numDeriv::jacobian`

function through a global option. For example:

`options(marginaleffects_numDeriv = list(method = "simple", method.args = list(eps = 1e-6)))`

`options(marginaleffects_numDeriv = list(method = "Richardson", method.args = list(eps = 1e-5)))`

`options(marginaleffects_numDeriv = NULL)`

See the "Standard Errors and Confidence Intervals" vignette on the `marginaleffects`

website for more details on the computation of standard errors:

https://vincentarelbundock.github.io/marginaleffects/articles/uncertainty.html

Note that the `inferences()`

function can be used to compute uncertainty estimates using a bootstrap or simulation-based inference. See the vignette:

https://vincentarelbundock.github.io/marginaleffects/articles/bootstrap.html

## Model-Specific Arguments

Some model types allow model-specific arguments to modify the nature of
marginal effects, predictions, marginal means, and contrasts. Please report
other package-specific `predict()`

arguments on Github so we can add them to
the table below.

https://github.com/vincentarelbundock/marginaleffects/issues

Package | Class | Argument | Documentation |

`brms` | `brmsfit` | `ndraws` | brms::posterior_predict |

`re_formula` | brms::posterior_predict | ||

`lme4` | `merMod` | `re.form` | lme4::predict.merMod |

`allow.new.levels` | lme4::predict.merMod | ||

`glmmTMB` | `glmmTMB` | `re.form` | glmmTMB::predict.glmmTMB |

`allow.new.levels` | glmmTMB::predict.glmmTMB | ||

`zitype` | glmmTMB::predict.glmmTMB | ||

`mgcv` | `bam` | `exclude` | mgcv::predict.bam |

`robustlmm` | `rlmerMod` | `re.form` | robustlmm::predict.rlmerMod |

`allow.new.levels` | robustlmm::predict.rlmerMod | ||

`MCMCglmm` | `MCMCglmm` | `ndraws` |

## Bayesian posterior summaries

By default, credible intervals in bayesian models are built as equal-tailed intervals. This can be changed to a highest density interval by setting a global option:

`options("marginaleffects_posterior_interval" = "eti")`

`options("marginaleffects_posterior_interval" = "hdi")`

By default, the center of the posterior distribution in bayesian models is identified by the median. Users can use a different summary function by setting a global option:

`options("marginaleffects_posterior_center" = "mean")`

`options("marginaleffects_posterior_center" = "median")`

When estimates are averaged using the `by`

argument, the `tidy()`

function, or
the `summary()`

function, the posterior distribution is marginalized twice over.
First, we take the average *across* units but *within* each iteration of the
MCMC chain, according to what the user requested in `by`

argument or
`tidy()/summary()`

functions. Then, we identify the center of the resulting
posterior using the function supplied to the
`"marginaleffects_posterior_center"`

option (the median by default).

## Equivalence, Inferiority, Superiority

\(\theta\) is an estimate, \(\sigma_\theta\) its estimated standard error, and \([a, b]\) are the bounds of the interval supplied to the `equivalence`

argument.

Non-inferiority:

\(H_0\): \(\theta \leq a\)

\(H_1\): \(\theta > a\)

\(t=(\theta - a)/\sigma_\theta\)

p: Upper-tail probability

Non-superiority:

\(H_0\): \(\theta \geq b\)

\(H_1\): \(\theta < b\)

\(t=(\theta - b)/\sigma_\theta\)

p: Lower-tail probability

Equivalence: Two One-Sided Tests (TOST)

p: Maximum of the non-inferiority and non-superiority p values.

Thanks to Russell V. Lenth for the excellent `emmeans`

package and documentation which inspired this feature.

## Examples

```
if (FALSE) {
# Adjusted Prediction for every row of the original dataset
mod <- lm(mpg ~ hp + factor(cyl), data = mtcars)
pred <- predictions(mod)
head(pred)
# Adjusted Predictions at User-Specified Values of the Regressors
predictions(mod, newdata = datagrid(hp = c(100, 120), cyl = 4))
m <- lm(mpg ~ hp + drat + factor(cyl) + factor(am), data = mtcars)
predictions(m, newdata = datagrid(FUN_factor = unique, FUN_numeric = median))
# Average Adjusted Predictions (AAP)
library(dplyr)
mod <- lm(mpg ~ hp * am * vs, mtcars)
avg_predictions(mod)
predictions(mod, by = "am")
# Conditional Adjusted Predictions
plot_predictions(mod, condition = "hp")
# Counterfactual predictions with the `variables` argument
# the `mtcars` dataset has 32 rows
mod <- lm(mpg ~ hp + am, data = mtcars)
p <- predictions(mod)
head(p)
nrow(p)
# average counterfactual predictions
avg_predictions(mod, variables = "am")
# counterfactual predictions obtained by replicating the entire for different
# values of the predictors
p <- predictions(mod, variables = list(hp = c(90, 110)))
nrow(p)
# hypothesis test: is the prediction in the 1st row equal to the prediction in the 2nd row
mod <- lm(mpg ~ wt + drat, data = mtcars)
predictions(
mod,
newdata = datagrid(wt = 2:3),
hypothesis = "b1 = b2")
# same hypothesis test using row indices
predictions(
mod,
newdata = datagrid(wt = 2:3),
hypothesis = "b1 - b2 = 0")
# same hypothesis test using numeric vector of weights
predictions(
mod,
newdata = datagrid(wt = 2:3),
hypothesis = c(1, -1))
# two custom contrasts using a matrix of weights
lc <- matrix(c(
1, -1,
2, 3),
ncol = 2)
predictions(
mod,
newdata = datagrid(wt = 2:3),
hypothesis = lc)
# `by` argument
mod <- lm(mpg ~ hp * am * vs, data = mtcars)
predictions(mod, by = c("am", "vs"))
library(nnet)
nom <- multinom(factor(gear) ~ mpg + am * vs, data = mtcars, trace = FALSE)
# first 5 raw predictions
predictions(nom, type = "probs") |> head()
# average predictions
avg_predictions(nom, type = "probs", by = "group")
by <- data.frame(
group = c("3", "4", "5"),
by = c("3,4", "3,4", "5"))
predictions(nom, type = "probs", by = by)
# sum of predicted probabilities for combined response levels
mod <- multinom(factor(cyl) ~ mpg + am, data = mtcars, trace = FALSE)
by <- data.frame(
by = c("4,6", "4,6", "8"),
group = as.character(c(4, 6, 8)))
predictions(mod, newdata = "mean", byfun = sum, by = by)
}
```